Proportional hazards model with a change point for clustered event data.

In many epidemiology studies, family data with survival endpoints are collected to investigate the association between risk factors and disease incidence. Sometimes the risk of the disease may change when a certain risk factor exceeds a certain threshold. Finding this threshold value could be important for disease risk prediction and diseases prevention. In this work, we propose a change-point proportional hazards model for clustered event data. The model incorporates the unknown threshold of a continuous variable as a change point in the regression. The marginal pseudo-partial likelihood functions are maximized for estimating the regression coefficients and the unknown change point. We develop a supremum test based on robust score statistics to test the existence of the change point. The inference for the change point is based on the m out of n bootstrap. We establish the consistency and asymptotic distributions of the proposed estimators. The finite-sample performance of the proposed method is demonstrated via extensive simulation studies. Finally, the Strong Heart Family Study dataset is analyzed to illustrate the methods.